Existence of a solution to a stationary quasi-variational inequality with a lower order term in a multiply-connected domain with holes

Abstract

We consider a stationary quasi-variational inequality in a multiply-connected domain with holes and show the existence of a solution to the inequality. The problem is related to the Bean critical-state model in type II superconductors. Mathematically, we are concerned with a quasi-variational inequality containing a p-curlcurl inequality with a curl constraint by a function of the solution.